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What is the inertial force in fluids?

Important Questions on Mechanical Properties of Fluids

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Water from a pipe is coming at a rate of

100

liters per minute. If the radius of the pipe is

5 c m,

the Reynolds number for the flow is of the order of: (density of water =

100 k g / m^{3},

coefficient of viscosity of water

= 1 m P a s)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A air bubble of radius

1 cm

in water has an upward acceleration of

9.8 cm s^{- 2}

. The density of water is

1 gm {cm}^{- 3}

and water offers negligible drag force on the bubble. The mass of the bubble is

(g = 980 cm / s^{2})

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Air (density

ρ

) is being blown on a soap film (surface tension

T

) by a pipe of radius

R

with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed

v

\frac{1}{2} ρ v^{2},

the speed at which the bubble formed is

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Consider the configuration of a stationary water tank of cross-section area $A_{0}$ and a small bucket as shown in figure below;

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What should be the speed $v$ of the bucket, so that the water leaking out of a hole of cross-section area $A$ (as shown) from the water tank does not fall outside the bucket?

(Take, $h = 5 m, H = 5 m, g = 10 m s^{- 2}, A = 5 {cm}^{2}$ and $A_{0} = 500 {cm}^{2}$ ).

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

p

is the density and

η

is coefficient of viscosity of fluid which flows with a speed

v

in the pipe of diameter

d

, the correct formula for Reynolds number

R_{e}

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A bubble of radius

R

in water of density

ρ

is expanding uniformly at speed

v

. Given that water is incompressible, the kinetic energy of water being pushed is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A very large block of ice of the size of a volleyball court and of uniform thickness of

8 m

is floating on water. A person standing near its edge wishes to fetch a bucketful of water using a rope. The smallest length of rope required for this is about

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

The velocity of water in a river is

18 km h^{- 1}

near the surface. If the river is

5 m

deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water

= 10^{- 2} poise

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Statement (A): When the temperature increases the viscosity of gases increases and the viscosity of liquids decreases.

Statement (B): Water does not wet an oily glass because cohesive force of oil is less than that of water.

Statement (C) : A liquid will wet a surface of a solid if the angle of contact is greater than $90 °$ .

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A glass capillary tube is of the shape of a truncated cone with an apex angle

α

so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height

h

, where the radius of its cross-section is

b

. If the surface tension of water is

S

, its density is

ρ

, and its contact angle with glass is

θ

, then the value of

h

will be (

g

is the acceleration due to gravity)

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

The platelets are drifting with the blood flowing in a streamline flow through a horizontal artery as shown below:

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Artery is contracted in region $II$ . Choose the correct statement.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Under a constant pressure head, the rate of flow of orderly volume flow of liquid through a capillary tube is

V .

if the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18 L {(\min)}^{- 1}$ to $0.48 L {(\min)}^{- 1} ?$ The radius of the tap and viscosity of water are $0.5 cm$ and $10^{- 3} Pa s$ , respectively. (Density of water : $10^{3} kg m^{- 3}$ )

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Consider the wall of a dam to be straight with height

H

and length

L

. It holds a lake of water of height

h (h < H)

on one side. Let the density of water be

ρ_{w}

Denote the torque about the axis along the bottom length of the wall by

τ_{1}

. Denote also a similar torque due to the water up to height

\frac{h}{2}

and wall length

\frac{L}{2}

τ_{2}

. Then,

\frac{τ_{1}}{τ_{2}}

(ignore atmospheric pressure) is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Consider a thin square plate floating on a viscous liquid in a large tank. The height

h

of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity

u_{0}

. Which of the following statements is (are) true?

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A steel ball is dropped in a viscous liquid. The distance of the steel ball from the top of the liquid is shown below. The terminal velocity of the ball is closest to

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MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A solid sphere of volume

V

experiences a viscous force

F

when descending with a speed

v

in a liquid. If another solid sphere of volume

27 V

descends with the same speed

v

in the same liquid, it experiences a viscous force

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A hollow spherical shell at outer radius

R

floats just submerged under the water surface. The inner radius of the shell is

r .

If the specific gravity of the shell material is

\frac{27}{8}

with respect to water, the value of

r

is:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Identify the incorrect statement regarding Reynold's number

(R_{e}) :

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter

\frac{2}{\sqrt{π}} c m

then the Reynolds number for the flow is (density of water =

10^{3} k g / m^{3} a n d v i s c o s i t y o f w a t e r = 10^{- 3} P a . s

) close to:

What is the inertial force in fluids?

Important Questions on Mechanical Properties of Fluids

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